Problem: What do the following two equations represent? $-3x+y = -1$ $6x-2y = -3$
Explanation: Putting the first equation in $y = mx + b$ form gives: $-3x+y = -1$ $y = 3x-1$ Putting the second equation in $y = mx + b$ form gives: $6x-2y = -3$ $-2y = -6x-3$ $y = 3x + \dfrac{3}{2}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.